Digital transmission over a channel requires equalization of the channel's response over the frequency spectrum used by the transmitted information. A channel's impulse response is defined as the pulse resulting from the application of an impulse of unit value to the channel. When a channel is properly equalized, symbols preceding and following the symbol of interest contribute nothing to that signal, i.e., there is no inter-symbol interference at the moment when the signal of interest is sampled. Equalization is commonly performed by digital signal processing after the analog waveform received by the subscriber's modem has been quantized by a high precision analog to digital (A/D) converter in the modem at a sufficiently high sampling rate to avoid aliasing distortion. A popular method of equalization is accomplished by passing the digital signal through an adaptive filter and updating each filter tap coefficient in a direction opposite to the derivative of the mean square error signal for that tap. This method is also referred to as the least mean squared (LMS) method of adaptation.
When the receiving modem is digitally connected to the network, the function of the A/D converter in the modem is replaced by a limited precision A/D converter at the network subscriber line interface and the digital signal presented to the adaptive filter includes whatever error was introduced because of the difference between the network codec's limited set of discrete slicing levels and the actual amplitude of the received analog signal. The amplitude difference to the nearest quantization level is called the quantization error. This error in .mu.-law and A-law codecs is different for each amplitude of transmitted signal. As a result, the response that needs to be equalized includes the quantization error characteristics of the network A/D converter, as well as that of the physical channel, e.g., the subscriber loop. While the subscriber loop can be reasonably well modeled with a linear response over the voice band, important non-linear impairments are present in the A/D and D/A converters. It has been observed that PCM A-law or .mu.-law encoding introduces about 37-38 dB of quantization noise. This quantization noise sets an upper limit to the transmission speeds obtainable using traditional modem modulation techniques, such as CCITT V.34.
In U.S. Pat. No. 5,394,437, assigned to the assignee of the present application, a high speed modem is described which is synchronized to the sampling times of the PCM codec and which also transmits analog signals at the same discrete amplitude levels as are employed by the codec. Recently, there has been substantial interest in the "56k" modems developed using the techniques in this patent Early products have only achieved higher speed operation in the server modem to client modem direction. This is no surprise as the practical challenges of achieving high speed operation in the reverse direction are greater as the contents of this application will illustrate. The procedures of U.S. Pat. No. 5,394,437 minimize or eliminate the effects of quantization noise once the system has been "trained" and, for this, the impulse response of the channel in the direction from the customer's modem to the network codec must first have been accurately identified. This is accomplished during a training interval. But during the training interval the PCM codec introduces quantization noise, so at first glance it appears that the channel impulse response cannot be ascertained to an accuracy better than the 38 dB signal to noise ratio introduced by the codec. Since the achievement of data rates greater than what are available with current generation of V.34 or "56k" modems in the client-to-server direction require a signal to nose ratio better than 38 dB it would be of great utility to provide a method for more accurately ascertaining the impulse response of a channel and then equalizing the channel despite the presence of codec quantization noise.